Sensei’s library actually has some rather useful examples for this discussion. I started at the article on the one-point jump:
Common in running fights, the one-point jump moves out quickly (see getting ahead with a one-point jump), but is potentially vulnerable to being cut depending on the surrounding position (see cutting the one-point jump).
The page on cutting the one-point jump is brief but was well worth it. It led me to the rather dense page called don’t try to cut the one-point jump:
The cut may work, but often the damage to your own stones is bigger than to the opponents’.
This included a discussion about how cutting the one-point jump will leave you with two separate cutting stones both of which are vulnerable to attack. I’d recommend checking it out in more detail but, really, the page was summed up nicely by one of the users:
thanatos13: the proverb should be “only try to cut the one point jump when you are as strong as a Big Grizzly Bear on both sides.”
I was trying to incorporate @david265’s question into this post by suggesting that the one-point jump could lend itself to an eventual table-shape but I got a bit lost making anything tangible come together. That did, however, turn me towards the best example I found about this, which was the stretch as good shape page.
Check this out:
In this position, the cautious stretch (or, better, stand) of White 1 is the standard way for White to come out into the centre.
In the ideal world, we’d want to do a one-point jump to get out faster, but Black is strong either side and the original three-stones are already only tenuously connected.
White 1 here is a shape involving a dangerous chance for Black to cut, combining plays at a and b.
So the one-point jump is a great move and works in most situations where you have some space either side. That’s because if you have such space, you can likely capture your opponent’s stones should they try to cut. However, as the game progresses, keep an eye on your one-point jumps. If your opponent builds strength either side of your stones you may need to return and bolster your connection - and if your opponent is already strong then maybe it’s not the right choice in the first place.